I learned a new term recently that I think is very relevant in corporate growth and success, intrepreneur. The intrepreneur is the baby brother to the entrepreneur. This is the guy who has that big idea and wants to change the world; he has the mentality to do so but doesn't have the resources. Resources, in fact, is the only way in which they differ. The entrepreneur finds a way to resource his idea, but whether due to motivation or circumstance, the intrepreneur can't quite get over that issue. Often times these are the shooting stars in your organization. The trick is to enable these guys to make things happen. Give them the resources and turn them loose. The 20% time mentioned above is a great way of finding these individuals. The successful intrepreneur will gather others and use their 20% time to make something cool. What engineer do you know that wouldn't consider that paradise?

Why are engineers so important to America's success? Here is an interesting fact or two: Google hires 50% engineers and 50% everyone else. Twice as many start-up businesses are from new MIT grads than from Harvard Business School graduates (and the schools are practically right next to each other). I haven't met an engineer who doesn't like to make cool things; it is in their mindset; it is in their nature; great engineers usually make pretty good money relative to the average Joe in America, simply because their skill set is so valued. Thing is, they aren't always the top-paid people, even though their contributions are often much more critical to success than that of all the management above them. I think this is because they get so much satisfaction out of making stuff that, as long as they feel like they are making ends meet, things are good. This type of person is a huge asset to the American economy. Greed doesn't drive them, invention does, and invention leads to an improved economy more than anything else. Invention of new technology improves the standard of living for everyone. It is the only thing that does.

Google went from nothing to the top in 11 years; they themselves credit this to hiring great engineers and cutting them loose to change the world. We need more of this. We humans have a built-in engineering gene; we love to build and make stuff. Every kid plays with blocks, creates things, and imagines things. So why aren't there more engineers? Is it really that hard to become one? Should it be? I hope that somebody out there reads this book and thinks, “Screw all those guys who think I'm not smart enough—I'm gonna change the world anyway!”

Granted, there are many good teachers out there and you might have gotten the basics, but time and too many “status reports” have dulled the finish on your basic knowledge set. If you are like me, you have found a few really good books that you often pull off the shelf in times of need. They usually have a well-written, easy-to-understand explanation of the particular topic you need to apply. I hope this will be one of those books for you.

You might also be a fish out of water, an ME thrown into the world of electrical engineering, who would really like a basic understanding to work with the EEs around you. If you get a really good understanding of these principles, I guarantee you will surprise at least some of the “sparkies” (as I like to call them) with your intuitive insights into the problems at hand.

I don't mean to knock the collegiate educational system, but it seems to me that too often we can pass a class in school with the “assimilate and regurgitate” method. You know what I mean: Go to class, soak up all the things the teacher wants you to know, take the test, say the right things at the right time, and leave the class without an ounce of applicable knowledge. I think many students are forced into this mode when teachers do not take the time to lay the groundwork for the subject they are covering. Students are so hard-pressed to simply keep up that they do not feel the light bulb go on over their heads or say, “A-ha, now I get it!” The reality is, if you leave the class with a fundamental understanding of the topic and you know that topic by heart, you will be eminently more successful at applying that basic knowledge than anything from the end of the syllabus for that class.

The job of the engineering manager¹ really should have more to it than is depicted by the pointy-haired boss you see in Dilbert cartoons. One thing many managers do not know about engineers is that they welcome truly insightful takes on whatever they might be working on. Please notice I said “truly insightful;” you can't just spout off some acronym you heard in the lunchroom and expect engineers to pay attention. However, if you understand these basics, I am sure there will be times when you will be able to point your engineers in the right direction. You will be happy to keep the project moving forward, and they will gain a new respect for their boss. (They might even put away their pointy-haired doll!)

Please don't get me wrong, I don't mean to say that all teachers are bad; in fact, most of my teachers (barring one or two) were really good instructors. However, sometimes I think the system is flawed. Given pressures from the dean to cover X, Y, and Z topics, sometimes the more fundamental X and Y are sacrificed just to get to topic Z.

I did get a chance to teach a semester at my own alma mater. Some of these chapters are directly from that class. My hope for teachers is to give you another tool that you can use to flip the switch on the “a-ha” light bulbs over your students' heads.

At the end of each topic discussed in this book are bullet points I like to call Thumb Rules. They are what they seem: those “rule-of-thumb” concepts that really good engineers seem to just know. These concepts are what always led them to the right conclusions and solutions to problems. If you get bored with a section, make sure to hit the Thumb Rules anyway. There you will get the distilled core concepts that you really should know.

Which came first, the chicken or the egg? I was faced with just such a quandary when I set down to create the original edition of this book. The way that I found people got the most out of the topics was to get some basic ideas and concepts down first; however, those ideas were built on a presumption of a certain amount of knowledge. On the other hand, I realized that the knowledge that was to be presented would make more sense if you first understood these concepts—thus my chicken-versus-egg dilemma.

Suffice it to say that I jumped ahead to explaining the chicken (the chicken being all about using electricity to our benefit). I was essentially assuming that the reader knew what an egg was (the “egg” being a grasp on what electricity is). Truth be told, it was a bit of a cheat on my part, ¹ and on top of that I never expected the book to be such a runaway success. Turns out there are lots of people out there who want to know more about the magic of this ever-growing electronic world around us. So, for this new and improved edition of the book, I will digress and do my best to explain the “egg.” Skip ahead if you have an idea of what it's all about, ² or maybe stick around to see if this is an enlightening look at what electricity really is.

The electron—what is it? Well, we haven't ever seen one, but we have found ways to measure a bunch of them. Meters, oscilloscopes, and all sorts of detectors tell us how electrons move and what they do. We have also found ways to make them turn motors, light up light bulbs, power cell phones, computers, and thousands of other really cool things. The impact on our society is immeasurable, it goes to the very core, we even use the symbol of a light bulb turning on as an analogy to having a great idea. Not bad for something that only became part of the world at large a little over 100 years ago. Ironically it is this very light bulb I hope to metaphorically turn on for the readers of this book.

What is electricity though? Actually, that is a very good question. If you dig deep enough you can find RSPs³ all over the world who debate this very topic. I have no desire to that join that debate (having not attained RSP status yet). So I will tell you the way I see it and think about it so that it makes sense in my head. Since I am just a hick from a small town, I hope that my explanation will make it easier for you to understand as well.

We need to begin by learning about a very small particle that is referred to as an atom. A simple representation of one is shown in Figure 0.1.

Atoms⁴ are made up of three types of particles: protons, neutrons, and electrons. Only two of these particles have a feature that we call charge. The proton carries a positive charge and the electron carries a negative charge, whereas the neutron carries no charge at all. The individual protons and neutrons are much more massive than the wee little electron. Although they aren't the same size, the proton and the electron do carry equal amounts of opposite charge.

Now, don't let the simple circles of my diagram lead you to believe that this is the path that electrons move in. They actually scoot around in a more energetic 3D motion that physicists refer to as a shell. There are many types and shapes of shells, but the specifics are beyond the scope of this text. You do need to understand that when you dump enough energy into an atom, you can get an electron to pop off and move fancy free. When this happens the rest of the atom has a net positive charge⁵ and the electron a net negative charge. ⁶ Actually, they have these charges when they are part of the atom. They simply cancel each other out so that when you look at the atom as a whole the net charge is zero.

Now, atoms don't like having electrons missing from their shells, so as soon as another one comes along it will slip into the open slot in that atom's shell. The amount of energy or work it takes to pop one of these electrons loose depends on the type of atom we are dealing with. When the atom is a good insulator, such as rubber, these electrons are stuck hard in their shells. They aren't moving for anything. Take a look at the sketch in Figure 0.2.

In an insulator, these electron charges are “stuck” in place, orbiting the nucleus of the atom—similar to water frozen in a pipe. ⁷ Do take note that there are just as many positive charges as there are negative charges.

With a good conductor though, such as copper, the electrons in the outer shells of the atoms will pop off at the slightest touch; in metal elements these electrons bounce around from atom to atom so easily that we refer to them as an electron sea, or you might hear them referred to as free electrons. More visuals of this idea are shown in Figure 0.3.

You should note that there are still just as many positive charges as there are negative charges. The difference now is not the number of charges; it is the fact that they can move easily. This time they are like water in the pipe that isn't frozen but liquid—albeit a pipe that is already full of water, so to speak. Getting the electrons to move just requires a little push and away they go. ⁸ One effect of all these loose electrons is the silvery-shiny appearance that metals have. No wonder the element that we call silver is one of the best conductors there is.

One more thing: A very fundamental property of charge is that like charges repel and opposite charges attract. ⁹ If you bring a free electron next to another free electron, it will tend to push the other electron away from it. Getting the positively charged atoms to move is much more difficult; they are stuck in place in virtually all solid materials, but the same thing applies to positive charges as well. ¹⁰

So now we have an idea of what insulators and conductors are and how they relate to electrons and atoms. What is this information good for, and why do we care? Let's focus on these charges and see what happens when we get them to move around.

First, let's get these charges to move to a place and stay there. To do this we'll take advantage of the cool effect that these charges have on each other, which we discussed earlier. Remember, opposite charges attract, whereas the same charges repel. There is a cool, mysterious, magical field around these charges. We call it the electrostatic field. This is the very same field that creates everything from static cling to lightning bolts. Have you ever rubbed a balloon on your head and stuck it on the wall? If so, you have seen a demonstration of an electrostatic field. If you took that a little further and waved the balloon closely over the hair on your arm, you might notice how the hairs would track the movement of the balloon. The action of rubbing the balloon caused your head to end up with a net total charge on it and the opposite charge on the balloon. The act of rubbing these materials together¹¹ caused some electrons to move from one surface to the other, charging both your head and the balloon.

This electrostatic field can exert a force on other things with charges. Think about it for a moment: If we could figure out a way to put some charges on one end of our conductor, that would push the like charges away and in so doing cause those charges to move.

Figure 0.4 shows a hypothetical device that separates these charges. I will call it an electron pump and hook it up to our copper conductor we mentioned previously.

In our electron pump, when you turn the crank, one side gets a surplus of electrons, or a negative charge, and on the other side the atoms are missing said electrons, resulting in a positive charge. ¹²

If you want to carry forward the water analogy, think of this as a pump hooked up to a pipe full of water and sealed at both ends. As you turn the pump, you build up pressure in the pipe—positive pressure on one side of the pump and negative pressure on the other. In the same way, as you turn the crank you build up charges on either side of the pump, and then these charges push out into the wire and sit there because they have no place to go. If you hook up a meter to either end you would measure a potential (think difference in charge) between the two wires. That potential is what we call voltage.

Okay, it's later now. We find that another very cool thing happens when we move these charges. Let's go back to our pump and stick a light bulb on the ends of our wires, as shown in Figure 0.5.

Remember that opposite charges attract? When you hook up the bulb, on one side you have positive charges, on the other negative. These charges push through the light bulb, and as they do they heat up the filament and make it light up. If you stop turning the electron pump, this potential across the light bulb disappears and the charges stop moving. Start turning the pump and they start moving again. The movement of these charges is called current. ¹⁴ The really cool thing that happens is that we get another invisible field that is created when these charges move; it is called the electromagnetic field. If you have ever played with a magnet and some iron filings, you have seen the effects of this field. ¹⁵

So, to recap, if we have a bunch of charges hanging out, we call it voltage, and when we keep these charges in motion we call that current. Some typical water analogies look at voltage as pressure and current as flow. These are helpful to grasp the concept, but keep in mind that a key thing with these charges and their movements is the seemingly magical fields they produce. Voltage generates an electrostatic field (it is this field repelling or attracting other charges that creates the voltage “pressure” in the conductor). Current or flow or movement of the charges generates a magnetic field around the conductor. It is very important to grasp these concepts to enhance your understanding of what is going on. When you get down to it, it is these fields that actually move the work or energy from one end of a circuit to another.

Let's go back to our pump and light bulb for a minute, as shown in Figure 0.6.

Turn the pump, and the bulb lights up. Stop turning and it goes out. Start turning and it immediately lights up again. This happens even if the wires are long! We see the effect immediately. Think of the circuit as a pair of pulleys and a belt. The charges are moving around the circuit, transferring power from one location to another—see Figure 0.7. ¹⁶

Fundamentally, we can think of the concept as shown in the drawing in Figure 0.8.

Even if the movement of the belt is slow, ¹⁷ we see the effects on the pulley immediately, at the moment the crank is turned. It is the same way with the light bulb. However, the belt is replaced by the circuit, and it is actually the electromagnetic¹⁸ fields pushing charges around that transmit the work to the bulb. Without the effects of both of these fields, we couldn't move the energy input at the crank to be output at the light bulb. It just wouldn't happen.

Like the belt on the pulleys, the charges move around in a loop. But the work that is being done at the crank moves out to the light bulb, where it is used up making the light shine. Charges weren't used up; current wasn't used up. They all make the loop (just like the belt in the pulley example). It is energy that is used up. Energy is work; you turning the crank is work. The light bulb takes energy to shine. In the bulb, energy is converted into heat on the filament that makes it glow so bright that you get light. But remember, it is energy that it takes to make this happen. You need both voltage and current (along with their associated fields) to transfer energy from one point to another in an electric circuit.

Now, all the electronic items that we are going to learn about are based on these charges and their movement. We will learn about resistance—the measurement of how difficult it is to get these electrons to pop loose and move around a circuit. We will learn about a diode, a device that can block these charges from moving in one direction while letting them pass in another. We will learn about a transistor and how (using principles similar to the diode) it can switch a current flow on and off. ¹⁹

We will learn about generators and batteries and find out they are simply different versions of the electron pump that we just talked about.

We will learn about motors, resistors, lights, and displays—all items that consume the power that comes from our electron pump.

But just remember, it all comes back to this basic concept of a charge, the fields around it when it sits there, and the fields that are created when the charges move.

Once you grasp the idea of charges and how the presence and movement of these charges transfer energy, the magic of electricity is somewhat lost. If you get the way these charges are similar to a belt turning a pulley, you are already further ahead in understanding than I was when I graduated from college. Whatever you do, don't let anyone tell you that you can't learn²⁰ this stuff. It really isn't all that magical, but it does require you to have an imagination. You might not be able to see it, but you surely can grasp the fundamentals of how it works.

So give it a try; don't say you can't do this, ²¹ because I am sure you can. If you read this book and don't come away with a better grasp of all things electrical and electronic, please drop me a line and complain about it. As long as my inbox isn't too clogged by email from all those raving reviews, I will be sure to get back to you.

This is a skill that one of my favorite teachers drilled into me during my senior year. Until I understood unit math, I forced myself to memorize hundreds of equations just to pass tests. After applying this skill I found that, with just a few equations and a little algebra, you can solve nearly any problem. This was definitely an “a-ha” moment for me. Suddenly the world made sense. Remember those dreaded story problems that you had to do in physics? Using unit math, those problems become a breeze; you can do them without even breaking a sweat.

Mechanical engineers have it easy. They can see what they are working on most of the time. As an EE, you do not usually have that luxury. You have to imagine how those pesky electrons are flittering around in your circuit. We are going to cover some basic comparisons that use things you are familiar with to create an intuitive understanding of a circuit. As a side benefit, you will be able to hold your own in a mechanical discussion as well. There are several reasons to do this:

Electrons are everywhere, or maybe it is better said that the effects of electrons are everywhere. There are invisible fields of force all around us that are caused by those pesky little devils. These fields warrant discussion because they are a factor in the way we deal with electricity. They can store energy and affect the world around them in various ways, so it is good to build an intimate knowledge of these fields and how they interact. These are the same fields that we talked about in Chapter 0 of this edition. If you elected to skip it when you started reading and you feel a little lost here, I suggest going back to read it.

Now, we can't beam people³² on and off the planet like they do on Star Trek, but there are couple of invisible fields that are what actually create all the effects that we see in electric circuits. It is these fields that make the water, ping-pong ball, and many other analogies not quite match what is really going on in a circuit. So understanding these fields will definitely help develop the intuitive skills we are working on.

The topic of control theory is typically left until later in most education programs because it is considered a more advanced topic. Control systems, however, are a very common application in the electronic realm. Think about it; I'll bet most of the time you design a device to control something you don't want to think about, something that automatically does what it should without intervention. On top of that, control theory turns out to be useful in more than just clear-cut control applications—understanding op-amps and designing power supplies, for example. Since a basic knowledge of this concept will help you in many aspects of your career, it seems prudent to dedicate a few pages to it.

One thing in common with all electrical devices (this side of superconductors) is the fact that as they operate, heat is generated. This is because in every component (as we will learn later) there is some amount of equivalent resistance. Resistance times current flow equals a voltage drop, and a voltage drop times current equals power. Since Ohm's Law is unavoidable, this power must turn into heat. Heat is the premier cause of wear and tear in electronic components, so managing heat is a good thing to know something about. Let's start from the inside out.

If you didn't just finish reading them, go back and read the last section's thumb rules. They are very important in developing a correct understanding of what an op-amp does. Why are these points important? Let's go over a little history.

Up until the invention of op-amps, engineers were limited to the use of transistors in amplification circuits. The problem with transistors is that, being “current-driven” devices, they always affect the signal of the circuit that the designer wants to amplify by loading the circuit. Also, due to manufacturing tolerances of transistors, the gain of the circuits would vary significantly. All in all, designing an amplifier circuit was a tedious process that required much trial and error. What engineers wanted was a simple device that they could attach to a signal that could multiply the value by any desired amount. The device should be easy to use and require very few external components. To paraphrase, operation of this amplifier should be a “piece of cake.” At least that is the way I remember it. The other way the name operational amplifier, or op-amp, came into being was to describe the fact that these amplifiers were used to create circuits in analog computers, performing such operations as multiplication, among others.

To begin with, let's take a look at the special case I mentioned in the previous discussion. First, return to the previous block diagram and add a feedback loop, as shown in Figure 3.13.

You will see that I have represented the forward or open-loop gain with the value G and the feedback gain with the value H. The first thing you should notice is that the output is tied to the negative input. This is called negative feedback. What good is negative feedback? Let's try an experiment. Hold your hand an inch over your desk and keep it there. You are experiencing negative feedback right now. You are observing via sight and feel the distance from your hand to the desk. If your hand moves, you respond with a movement in the opposite direction. This is negative feedback. You invert the signal you receive via your senses and send it back to your arm. The same thing occurs when negative feedback is applied to an op-amp. The output signal is sent back to the negative input. A signal change in one direction at the output causes a V_sum to change in the opposite direction.

You should get an intuitive grasp of this negative feedback configuration. Look at the previous diagram and assume a value of 50,000 for G and a value of 1 for H. Now start by applying a 1 to the positive input. Assume that the negative input is at 0 to begin with. That puts a value of 1 at the input of the gain block G and the output will start heading for the positive rail. But what happens as the output approaches 1? The negative input also approaches 1. The output of the summing block is getting smaller and smaller. If the negative input goes higher than 1, the input to the gain block G will go negative as well, forcing the output to go in the negative direction. Of course, that will cause a positive error to appear at the input of the gain block G, starting the whole process over again. Where will this all stop? It will stop when the negative input is equal to the positive input. In this case, since H is 1, the output will also be 1.

You have learned (or will learn) this in control theory. Look at the basic control equation in reference to Figure 3.13:

What happens when G is very large?¹⁸ The 1 in the denominator becomes insignificant and the equation becomes:

H in this case is 1, ¹⁹ so it follows that:

or:

This is the special case in which you can assume that the inputs of the op-amp are equal. Apply it only when there is negative feedback. When feedback gain is 1, this also demonstrates another neat op-amp circuit: the voltage follower. Whatever voltage is put on the positive input will appear at the output.

Take a look at Figure 3.14. This is an op-amp in the negative feedback configuration. When you look at this, you should see a summer and an amplifier, just as in the previous drawing. In this configuration, you can make the assumption that the positive and negative inputs are equal.

Negative feedback is the case that is drilled into you in school and is the one that often causes confusion. It is a special case—a very widely used special case. Nonetheless, if you do not have negative feedback and the inputs and output are within operational limits, you must not assume that the inputs of the op-amp are equal.

Why is this negative feedback configuration used so much? Remember the reason that op-amps were invented? Amplifiers were tough to make. There had to be an easier way. Take a look at the control equation again:

I have already shown that for large values of G, the equation approximates:

You will see that the amplification of Vi depends on the value of H. For example, if we can make H equal 1/10, then it follows that:

or:

How do we go about doing that? Do you remember the voltage divider circuit? That would be very useful here, since we would like H to be the equivalent of dividing by 10. Let's insert the voltage divider circuit in place of H.

Notice that the input to the voltage divider comes from the output of the op-amp Vo. The output of the voltage divider goes to the negative input of the op-amp V−. Now, will the op-amp input V− affect the voltage divider circuit? No! It has high impedance. It will not affect the divider. (If you didn't get that, go back and read the “What Is an Op-Amp, Really?” section 'til you do!)

Since the input to the divider is hooked to a voltage source, and the output is not affected by the circuit, we can calculate the gain from Vo to V− very easily with the voltage divider rule shown in Figure 3.15.

Thus it follows that:

or, with a little algebra:

There you have it—the gain of this op-amp circuit. Let's look at it another way. Go back to the previous equation:

We learned that in this special case of negative feedback, we can assume that V− = V+. This is because the negative feedback loop is pushing the output around, trying to reach this state. So let's assume that Vi = V−, which is where the input to our amplifier will be hooked up. Now we can replace V+ with Vi, and the equation looks like the following:

What we really want to know is, what does the circuit do to Vi to get Vo? Let's do a little math to come up with this equation:

Please note that this is equal to 1/H. You see, the gain of this circuit is controlled by two simple resistors. Believe me, this is a whole lot easier to define and calculate than a transistor amplification circuit. As you can see, the operation of this amplifier is pretty easy to understand.

What is positive feedback? Let's take a look at a real-world example. You are hard at work one day when your boss stops by and says, “Hey, you should know that you've handled your project very well, and that new op-amp circuit you built is awesome!” After you bask in his praise for a while, you find yourself working even harder than before. ²⁰ This is positive feedback. The output is sent back to the positive input, which in turn causes the output to move further in the same direction. Let's look at the op-amp diagram again—see Figure 3.16.

Now we will do a little intuitive analysis. Don't forget the Thumb Rules we learned in the last two sections. Review them now if you need to.

Begin by applying 0 V to V_in. In this case the input is connected to V−. You also see that the output is connected via a resistor to a reference voltage, V_ref. What is the voltage at V−? Does the voltage at V− equal the voltage at V+? No! (Don't believe me? Check the Thumb Rules!)

What is the voltage at V+? That depends on two things: the voltage at V_ref and the output voltage of the amplifier, Vo. Does the V+ input load the circuit at all? No, it does not. To begin the analysis, let V_ref = 2.5 V, and assume that the output is equal to 0 V. Now what is the voltage at V+? What do you know—since Vo is equal to 0, we have a basic voltage divider again. Assume R_ref = 10 K and R_h = 100 K:

So now there is 2.275 V at V+ and 0 V at V−. What will the op-amp do? Let's refer to the op-amp block diagram we learned earlier—see Figure 3.17.

What do we have? V_sum is equal to V+ − V− or, in this case, V_sum = 2.275 V. Vo is equal to V_sum * G. The output will obviously go to the positive rail. (If this is not obvious to you, you need to review “What Is an Op-Amp, Really?” again.) Now we have Vo at the positive rail. Let's assume that it is 4 V for this particular op-amp. (Remember, the output rails depend on the op-amp used, and you should always refer to the datasheets for that information. 4 V used in this case is typical for an LM324 with a 0 to 5 V supply.)

The output is at 4 V and V− is at 0 V, but what about V+? It has changed. We must go back and analyze it again. (Do you feel like you are going in circles? You should. That is what feedback is all about; outputs affect inputs, which affect the outputs, and so on, and so on.) The analysis this time has changed slightly. It is no longer possible to use just the voltage divider rule to calculate V+. We must also use superposition.

In superposition, you set one voltage source to 0 and analyze the results, and then you set the other source to 0 and analyze the results. Then you add the two results together to get the complete equation. Let's do that now. We already know the result due to V_ref from our previous example. Figure 3.18 shows the positive feedback diagram again for reference.

Here is the result due to V_ref using the voltage divider rule:

Here is the result due to Vo using the voltage divider rule:

The result due to both is thus:

Now insert all the current values and we have:

Is this circuit stable now? Yes, it is. We have 0 V at V− and 2.64 V at V+. This results in a positive error, which, when amplified by the open-loop gain of the op-amp, causes the output to go to the positive rail. This is 4 V, which is the state that we just analyzed.

Now let's change something and see what happens. Let's start slowly ramping up the voltage at V−. At what point will the op-amp output change? Right after the voltage at V− exceeds the voltage at V+. This results in a negative error, causing the output to swing to the negative rail. And what happens to V+? It changes back to 2.275 V, as we calculated above. So how do we get the output to go positive again? We adjust the input to less than 2.275 V. The positive feedback reinforces the change in the output, making it necessary to move the input farther in the opposite direction to affect another change in the output.

The effect that I have just described is called hysteresis. It is an effect very commonly created using a positive feedback loop with an op-amp. “What is hysteresis good for?” you ask. Well, heating your house, for one thing. It is hysteresis that keeps your furnace from clicking on and off every few seconds. Your oven and refrigerator use this principle as well. In fact, the disk drive on the computer I used to write this paragraph uses hysteresis to store information.

One important item to note: The size of the hysteresis window depends on the ratio of the two resistors R_ref and Rh. In most typical applications, Rh is much larger than R_ref. If the signal at Vi is smaller than the window, it is possible to create a circuit that latches high or low and never changes. This is usually not desired and can be avoided by performing the preceding analysis and comparing the calculated limits to the input signal range.

Now that we have covered the three basic configurations of an op-amp, let's put together a simple circuit that uses them. Here, we have a voltage follower, hooked to a comparator using hysteresis, with an LED as an indicator (Figure 3.19). You should build this in your lab to gain an intuitive understanding of what has been discussed. Experiment with feedback changes in all parts of the circuit. Note that you can change the input potentiometers from 5 to 100 K without affecting the voltage at which the comparator switches.

This is one of the most rapidly changing fields in the electronics industry. You can purchase microcontrollers today with only six pins with just a few lines of memory at a cost of 25 cents and for just a few bucks more, high-end embedded processors that just a few years ago would have been labeled supercomputers. All this from the few semiconductor types we have discussed. I will not try to cover specific processors since there are libraries of books dedicated to understanding particular micros. Instead, I will try to cover some fundamental rules that can be applied in general.

Add a bunch of logic gates together and mix with some adders, instruction decoders, and memory cells. Hook it all up to some input/output pins, apply a clock source, and you get a microcontroller or microprocessor.

These two devices are very similar, and you will hear the names used somewhat interchangeably. Generally, however, the microcontroller is more all inclusive, with all the elements it needs to operate included in one piece of silicon, typically making them a little (but not much) more specialized. The microprocessor by contrast needs external memory and interface devices to operate. This makes it more open ended, allowing memory upgrades without changing the chip, for example. As this area of technology has progressed, the line of distinction between these two components has blurred considerably. Hence, much of the design philosophy needed to make the most of these devices is the same.

Awhile back I was explaining to my boss that software was written in layers; he looked at me and wondered why we would do that at all—seemed like a waste of time to him. Like extra work to have all those layers when it's not needed. What I realized is that in today's world SW (software) has become as ubiquitous as electricity itself; it is also as magical. Nowadays networks are common, and software is updated all the time. My phone, my computer, and even my treadmill are all getting software updates regularly. This has led to a complete misunderstanding by the layman of the complexity of software. To him or her it just takes care of itself. If we were making one product one time one layer of software would be sufficient, but the fact is that software is fundamentally integrated into more and more products in our everyday lives at an ever-increasing rate. To allow faster development, software engineers have created all sorts of tools. Now when I am speaking of software here, I am covering the full gambit of the term, including what we often call firmware, etc.—anything that executes lines of code. Building on this we will learn how and why software is layered and hopefully learn some more about general design and good practices when coding.

Take a look at Figure 3.34. At the bottom of the pile is the foundation, assembly or machine code. Machine code is the actual 1 and 0, true and false information that is processed in the CPU; assembly is one level slightly higher. I lump them together because not many write in machine code anymore. At the lowest level assembly is used; this is a set of mnemonics that represent the machine code, it which is turned into machine code by a piece of SW called an assembler. ³² It is a pretty direct translation from the mnemonic to the 1s and 0s the system can process.

The next level up is C code. C has pretty much won out at this level. There were others like Pascal and such that competed, but there are very few systems today that do not have a C compiler. C was designed around the same time Unix came into being (that kind of explains why it is so foundational to Apple's products). C and variants like C++ all use a compiler, which is something more complex than an assembler. A compiler makes decisions as it creates the run time file, choosing ways to create the machine code that actually runs on the CPU. The important aggregate thing to know is that while a compiler can affect the size of the code and the speed of execution, it is not a direct translation of the language written to the 1s and 0s. One very powerful aspect of C, though, is that you can slip in assembly code as you like when using it, giving you a tool that can reach down into the bowels of the system so to speak when you need it. C has become so ubiquitous that the most simple micros will have a C compiler, giving you the ability to use that language in systems without an OS (note that it is often used with an OS as well).

There is one trade off as you move up the SW mountain that happens over and over. You get speed of development and portability but at a cost of using more system resources in terms of RAM and ROM and processing power. For example, you write a piece of code for one micro using their assembly language, but then you have to change out the MCU for some reason. To redo that work in assembly is very time consuming; however, if it is written in C you can go through it relatively quickly (compared to rewriting the assembly version, that is) and run the new compiler on it to get what you need. You will get more bang for your buck using assembly, but at the sacrifice of development time and portability. Now generally speaking, if I told someone today the most important language for them to learn, it would be C. ³³ One reason for this is the effect of Moore's law, the cost of RAM, ROM, and CPU power keep falling as densities increase; in just the 6 years since this book came out, the costs of midrange MCUs has fallen 70–80%. That means you can write in the higher level C language without suffering a cost penalty in many cases. Even if it costs more, the cost savings of using a smaller MCU often will not offset the development costs of using assembly. I realize this is a different take on things than in my toothbrush controller example from earlier, but the world changes and we have to keep up. Assembly still has its place, and I still think you will get many benefits learning it. It will certainly help you understand what the machine that you are working on is doing, and if you want to take full advantage of it to make whatever gadget you are building amazing, that foundation will always help. I also know that it is typically easier for a programmer to climb up the software ladder than it is for one to come down from the top. If you want to build a really flexible organization, get the types who know the foundation well. One of my EEs put it this way, “to transition up you have to find that one command that does the 30 lines of code you would have written (often accomplished by a Google search), but to transition down, you need to understand how to write those 30 lines of code.”

Next up we encounter operating systems. These aren't exactly programming languages, but they are very important in the software mountain of layers. Operating systems were designed to disconnect the code writers from the hardware they are working on. The reason for doing that was to make the code interface common for many, many, many different developers. An OS will manage the hardware, handle the I/O, memory, and other system resources so that the code writer doesn't need to worry about it. You can, however, write script and macros that the OS will do as needed. Operating systems use things called drivers and APIs³⁴ to communicate with programs and with hardware in the system. Drivers are lower-level, typically C or assembly code that handle a piece of hardware, such as a USB port. Since software is layered, there needs to be a way to communicate between the layers from the OS to the programs; this is the job of an API.

On top of the OS layer are all sorts of programs—one type that changed the world was the browser. First invented to create a common interface for programs connected on the Internet, it quickly became a mainstay of our computers. To program for a browser, even higher level languages were created: Java, PHP, and so on. Programs to make programming easier are all over the place. For example, Adobe Flash is a tool that makes it easier for graphic artists to program web pages. However, still having limitations on the visual elements, Adobe created something called action script, which is yet an even higher level language for programming. As you move up the programming ladder you find that the language becomes more readable to the layperson. ³⁵ Some of these higher level languages became widely used, and variations were created for “regular” programming. For example, Google's Andriod is a GUI layer on Linux that is a Dalvik Java machine, which lets a huge crowd of Java programmers make slick graphic interfaces quickly.

As you climb up the software mountain you find that there are always trade-offs of speed and performance versus ease, quickness, and universality of design. If you can afford the faster processor, you can generally get to market faster, but ironically as this software mountain builds year after year, layer on layer, it opens up spaces for software to be rewritten to run better and faster. Google Chrome is an example of this; it is a browser recoded from the ground up to be quicker and faster than before. Apple's OSX Snow Leopard release trimmed nonessential layers to improve performance.

As you develop code you invariably add layers to avoid rewriting sections of code, but at some point it becomes unwieldy for the system it is running on. The trick for an engineer or technical manager is knowing the right balance between the factors—you need to understand product costs, development costs, and speed to market costs to pick the best path for success.

The whole point of these devices is to put something in just to get something out. So it stands to reason that it's worthwhile to devote a few words to this topic.

If this book had been written back when computers were analog, this section wouldn't even be needed. As it is, the proliferation of those pesky little digital chips gives it top billing. You need to bridge the gap between the analog and the digital at some point if you want to market your latest gadget as “way cool digital technology.” Knowing a bit about how to make the analog-to-digital leap seems like a good idea.

What is A-to-D conversion (or ADC)? Is it a religious experience? Is it the opposite of D-to-A conversion (or DAC)? A to D is all about taking the real world and making it into ones and zeros so that digital technology can manipulate it. You can reasonably say that D to A reverses the process. Here we will explore what this A to D to A is and what it is good for.

A while ago I was explaining my thoughts on the world being analog in nature to a fellow engineer. He emailed me the following response:

In many ways he is correct in his eloquent comments; however, he refers to our perception. We place the analog information from the world into “digital buckets.” (There are certainly levels between hot and cold, for example.) I think the reason we do this is to facilitate decision making, to limit the store of information, and to ease communication. We impose a digital perception when it makes sense to do so. A better phrase I could have used is something like, “The world is analog in nature, upon which we impose our digital perceptions.” With that in mind, let's look at some more of the nuts and bolts of A-to-D conversion. We'll start with the DAC and a simple comparator from a couple of pages back.

A simple comparator will output a high or low signal depending on whether one input was above or below the other (Figure 4.3). This is a great time to use a comparator, since digital circuits like obvious signals such as high and low. Let's drill the basic process of this circuit: You convert a digital number to a known analog level, compare that to an analog signal, and if it is close to the same value (here is where resolution counts), the digital number you output represents the analog value.

Let's do an example. You are converting an analog signal with the actual value of 4.45. You try outputting a 1 on your DAC. The comparator says “higher” (it does this by outputting a 1, or a high signal⁶). You then try outputting a 2. The comparator says “higher.” Now you try a 3, then a 4. Guess what the comparator says each time. That's right, it says “higher.” So what do you try next? Of course, you try a 5. Then the comparator says “lower.” Now your circuit knows that the value is between 4 and 5. At this point you pick one of these two values⁷ (assuming in this case that the DAC only outputs six discrete levels over a range from 0–5). The smaller the steps or increments that you can output with the DAC, the closer you can estimate the value of the analog signal. When you make the steps in the DAC smaller you increase the resolution of the signal.

There is a better and faster way than merely sweeping across all the values in the range. (We will increase the resolution of our DAC now to illustrate this point.) Start by making your first output on the DAC equal to ½ of the entire range. In this case you output 2.5 on the DAC. Now look at what the comparator says and make a logic decision (digital is good for this sort of thing). You can see whether the comparator says “higher,” and you can eliminate everything below 2.5. So you make your next output equal to half of the remaining range—in this case, you output 3.75. Look at the comparator again and eliminate some more possibilities (a high eliminates everything below the number, whereas a low eliminates everything above the number), then output half the remaining range. Repeat this process until you are out of resolution and you will have an approximation of the analog signal. This is a very fast way of converting an analog signal known as successive approximation. It is often used when high-speed analog-to-digital conversion is needed.

Did you notice that I often use the word approximation as the A-to-D process takes place? This is because a digital signal can never truly equal an analog signal; it must always draw the line somewhere. Do not forget that digital means that there are discrete steps involved. Analog has, by definition, infinite increments.

Now that you have the basic idea behind the A-to-D conversion process, let's look at some examples of DAC circuits to develop a more intuitive understanding. ⁸

This is a slick way to get a digital voltage level, and you can get the R2R ladder in a nice compact package, as shown in Figure 4.4. You must take care not to hook it up to any low-impedance devices without buffering, since its output level can be easily affected by external loads.

How does the ladder work? A digital byte is output to the ladder, which changes the voltage level to the input of the comparator. You should note that the MSB (most significant bit) has the most effect on the output. The LSB (least significant bit) affects the output the least. This works very well with the approximation method described earlier. You simply load the DAC value you want on the resistors and look at the output signal. It is very fast. The biggest downside is that it uses a lot of output pins. (The output pins must be able to sink or source sufficient current to work correctly.) One caution: Make sure your processor can handle the output load of the ladder. The Zilog processor I used in one application of this circuit years ago worked fine and even had an onboard comparator for the ADC process, but I did use every pin, leaving little room for additional signals if needed.

In this circuit, the duty cycle of the PWM signal is ramped up from 0% until it passes the value of the analog signal, as indicated by the comparator—see Figure 4.5. The analog voltage is represented by the percentage of the PWM signal when the comparator changes state. The RC filter must turn the PWM into basically an analog level. This means that the PWM must switch significantly faster than the speed of the signal you are trying to digitize.

This method relies on the transient response of the basic RC circuit (Figure 4.6). The step input causes the input to the comparator to increase according to the response time of the RC circuit. The output of the RC circuit is equal to Vi(1 − e^−(t/τ)). So if you know the value of tau, which is R * C, you can calculate the voltage based on the time it takes to pass the input. This can be tedious to calculate in some micros, but often high accuracy is not needed and a lookup table of the values can be implemented. In many cases, a lower-resistance discharge path is added to this circuit to ensure that the output of the RC circuit begins at zero.

The downsides to this circuit are the curve calculations, but the first three tau of the signal are a fairly linear approximation. Depending on the application, that might be good enough. (Review the connection between electronics and hand grenades way back at the beginning of Chapter 1 to see when things are “good enough.”) If your task isn't too demanding and you don't get too close to the upper rail, you can simply count time and toss out that complex calculation, making this a quick, cheap, and dirty ADC.

So there you have three easy ways to get a digital approximation of an analog signal. All these circuits are perfectly fine to use as DACs only.

One last thought: These days a built-in A/D converter is an increasingly common feature on a microcontroller. However, they nearly all work on the principle of using a DAC to make an ADC. Studying this section can help you to get an idea of what is really going on in there. The more you know about how it works on the inside, the better engineer you will be!

Before we get into the problems that parts can have, we need to introduce the concept of an equivalent circuit. It is pretty simple: To create an equivalent circuit, you represent all its idiosyncrasies with combinations of perfect components. This is good for two reasons: First and most obvious, it makes it possible to model the effects of the imperfections. Second, and most important in the World of Darren, is that seeing the combinations of the parts that make up a real component makes it easier for you to apply the basic understanding of the perfect parts to grasp what the real part is doing.

Most engineers want to overdesign, give themselves plenty of headroom, and use parts that are double or triple the spec they need. Usually the manager is there saying, “It needs to cost less or it won't sell,” or “Do you really, really need that part?” To be honest, the answer lies somewhere between these extremes.

Every engineer has their favorite batch of circuits, and I'm no exception. There are tons of circuit cookbooks out there that show how to implement no end of cool features. There are so many that you could spend all your time searching them and never getting anything done. I suggest you develop your own favorite basic circuits that you know well and intuitively understand. This is simply an extension of the Lego philosophy that we discussed way back at the beginning of the book. Here are a few of my favorites. These are in addition to all the circuits I have used as examples up to this point. One reason they make such good examples is that they are so useful.

I have just a few favorite circuit concepts. Get your own and know them well. You will be better served knowing a few circuit concepts inside-out than knowing thousands superficially.

Following this advice, several readers of the first edition sent in some of their favorite circuits. Without further ado, they are presented next.

Steve Petersen sent in the circuit shown in Figure 4.19, saying something about being fun for parties and the potential to add a delay circuit to really surprise someone¹⁶ when they picked up whatever interesting device the circuit was embedded in.

Travis Hayes sent in the diagram of a sleek little circuit, as shown in Figure 4.20, that uses the inverter oscillator from my list to drive a voltage doubler circuit. He said it was a pretty slick and inexpensive way to get a higher voltage for an LCD he was using. I'd have to agree!

Alan Tyger just might be as big a fan of op-amps as I am. He sent in the circuit diagram shown in Figure 4.21; it uses just such a device to store a piece of information.

Michael Covington¹⁷ sent in the cool circuit shown in Figure 4.22; it combines the fun of remote controls with a laser pointer. The 555 acts as a memory cell (not unlike Alan's circuit), but this one has the added bonus that you use a laser to control it. How cool is that! I don't know any engineer who doesn't like lasers, and I'm pretty sure they all have to control the remote when they are home watching TV.

Mike Angeli sent in this cool circuit in Figure 4.23. He said he used it to position a load using a potentiometer feedback (thus the high-impedance requirement).

Sam Nay sent in the circuit shown in Figure 4.24, saying he was always fascinated by the ability to transmit data without wires. I'll bet he hooks up the laser-controlled switch that we saw just moment ago. Also, I happen to know of a secret circuit that I am not at liberty to disclose that uses a variation of optical circuits not that different from this one to take biometric readings. Bet you wish I could show you that one, don't you!?

Finally, Mourly Thov sent in the circuit shown in Figure 4.25. He said he just thought it was a slick way to change the DC voltage (and have some power capacity, which could be an issue with the one Travis sent in), so if you find yourself in need of a different voltage that can move some current, try an idea like this one.

On a final note, I have to say that from my communication with these engineers, I think they all fall in the RSP¹⁸ category. Then again, maybe that is just because they emailed me and really liked the first edition of this book. Either way, I thank them for their submissions and completely absolve myself from any responsibility for these circuits actually working. I hope they bring you luck and help you to fill up a notebook with your favorite circuits.

Whatever you do with electronics, you are going to need power to accomplish it. It will be useful to understand the basics of power supplies, since you are nearly guaranteed to deal with them at some point in your career.

One thing that happens in the real world is moving stuff. Eliminating moving parts is a commonly sought-after goal in the world of electronics. However, I suspect that sometime in your career you will need to make things move and you will be thrust into the world of electromechanical devices. Considering that what I knew about motors when I left school could be written on the thin edge of a postage stamp, ²² I feel the need to cover some of the basics behind motors and a few other electromechanical devices here.

Often some sort of voltage feedback is used to maintain the output voltage of the control to a desired level. Remember that in the DC PM motor the speed of the output shaft is proportional to the voltage applied. That makes it nice for maintaining speed. However, if you flip back a few pages you will notice the IR component of that equation represents what are known as losses. These losses are burned up as heat across the resistance of the wire in the motor armature (plus a little in the brushes). The loss is proportional to the current (I) through the motor, and the current is proportional to the load on the motor shaft.

This means that as load varies on the motor, the amount of loss varies. This results in a change of speed. Think of it like this: The voltage that gets burned up as heat never makes it to spinning the motor shaft—see Figure 4.37.

There are two ways to compensate for this. One way is to use speed feedback to adjust the voltage output to the motor to maintain a constant speed. The other is to compensate for the losses themselves.

In most DC motor control designs, you will find a voltage feedback loop that does 90% of the speed control work. Then, external to that, you will find a speed feedback control loop that will compensate for the rest of the variation—see Figure 4.38.

Though it is generally a good idea to feed back the signal you want to control, there could be times you do not have that luxury, or maybe there are reasons you do not want to use speed feedback. If this is the case, you can use another speed control approximation called IR compensation—see Figure 4.39. This is a method in which you monitor the load on the motor by sensing the current through the motor. The loss due to heat is proportional to this current. If you know the resistance of the motor, you can calculate how much voltage turns into heat, never making it to the output shaft. Add this much voltage to the input to the motor and you have a fairly good approximate speed control and you didn't need a tachometer!

All in all, controlling a DC PM motor speed is one of the simplest motion-control problems to tackle, but it is simple only relative to the other options out there. It is still a significant “chunk o' learnin'” to swallow. For this reason I suggest starting here if you want to learn motion control before moving on to some of the other available motors.

You will run into many types of motors. People have been goofing around with different ways to make a motor nearly as long as they have been messing with electricity. Here is a bit of overview on some various types of DC motors.

One difficulty that electrical engineers have in general is that the electrons they work with are not something you can pick up, touch, or feel. (Okay, I take back the feel part—there are definitely voltage levels that you can feel!) In reality, you infer the electrons' existence based on how they affect objects. You don't see the current flowing in a light bulb; you see the heat generated by the current flowing in a light bulb. Given this, tools that can measure various attributes of electricity are invaluable in electrical engineering.

First, let me make a statement: Simulators are great tools (here it comes), but too often I see a major mistake made with a simulator. The engineer fires up the simulator, tries out his or her idea, gets it all designed, then proceeds to build a real circuit, only to find the circuit does not work as the simulation did. Here is where the mistake comes in: All too often the engineer spends all his or her time trying to figure out why the circuit isn't working right while implicitly trusting the simulator to spit out the correct answer. For some reason as soon as the circuit is modeled on a computer, it seems to be an engineer's nature to trust the result on the simulator without question. Doing so almost invariably leads to immense frustration and confusion. You should take this adage to heart: The real world isn't wrong; your simulation is. It is always true. If the results don't match, something in your simulation does not actually represent what is on the prototype in the lab. The simulation is a representation of the real world, not the other way around.

I was passing by the lab one day when I saw one of my technicians looking over the shoulder of one of the engineers who was doing a less than spectacular job of soldering components on a PCB. ⁹ He had but one comment. He said, “What we have here is an engineer trying to do a technician's job.” Then he sat down and proceeded to do a most excellent job of putting the board together.

On the chance that you might not have a skilled tech at your disposal, and due to the fact that I believe that the more you know about how the product you are designing goes together, the better designer you will be, here we will go over the basics of soldering.